4 Answers
4

Both are correct. To me, Ich esse gerne Pizza hints at a question like Was ist Dein Lieblingsessen, whereas Ich esse Pizza gern would be more appropriate as an answer to Magst Du Pizza? That is, I would put the important word (the one carrying new information) at the end of the phrase.

+1 , I'd like to add that the second alternative "Ich esse Pizza gern." is also a good response if another person just said that he or she doesn't like pizza. "Ich esse Pizza gern." then has a notion of "I don't get how one can't like it" whereas "Ich esse gern Pizza" would be a bit more doubtful as to whether you yourself are a bit weird for liking it... it is veeeeeeery subtle though, my subjective perception and it highly depends on intonation I guess
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EmanuelMar 7 '12 at 16:46